1 Incarnation + 12 Regenerations = A Time Lord's Life

Paul McGann isn't or wasn't playing a Time Lord "regenerated for the eighth time..." but rather a Time Lord regenerated for the seventh time. Do the math.

The 1st Doctor (portrayed by William Hartnell) regenerated into the 2nd Doctor (played by Patrick Troughton) making the Doctor's new persona the result of his first regeneration. Jon Pertwee portrayed the 3rd Doctor after his second regeneration. Tom Baker played the 4th Doctor after his third regeneration, followed by Peter Davison as the 5th Doctor in his fourth regeneration. Davison was followed by Colin Baker, the 6th Doctor in this fifth regeneration who was followed by Sylvester McCoy as the 7th Doctor in his sixth regeneration, with Paul McGann, the 8th Doctor in his seventh regeneration.

The Doctor incarnate, before his first regeneration, was born. All subsequent aspects of him, what we call, "the second Doctor" or "the third Doctor" and so on, these are one and the same being in regenerated forms. Incarnation is not the same as regeneration. Incarnation precedes regeneration, otherwise there is nothing, no form, no body, to generate again, or to regenerate. So when we say a Time Lord has regenerated for the eighth time, he or she is now living in their 9th persona.

I see this quite a bit... I try to use the term "incarnation" instead of "regeneration" when speaking about the Doctor's timeline. William Hartnell played the first incarnation of the Doctor, not the first regeneration because he hadn't regenerated yet.